When I run k3flasher, the dots trickle in the terminal, but the kindle is not recognised...

That error message is a bit too specific, as probably it's just not equipped with enough permissions. You didn't quote the full command line (given that your shell displays an informational prompt), but just to make sure: That has to be run with sufficient permissions, in the simplest case just run it as root (either by using "sudo" or "su" from a simple user account).

By the way, a reasonably equipped Linux distribution will come with the "lsusb" tool which should show you the Kindle in its USB downloader mode as a device called "Freescale <mumblesomething> SE Ringo" (from the top of my head).